Question #5d860

1 Answer
Apr 13, 2016

Answer:

#"pH" = 4.6#

Explanation:

The pH of a solution is simply of measure of how many hydronium cations, #"H"_3"O"^(+)#, it contains.

More specifically, you can find a solution's pH by taking the negative log base #10# of the concentration of hydronium cations present in solution.

#color(blue)(|bar(ul(color(white)(a/a)"pH" = - log( ["H"_3"O"^(+)])color(white)(a/a)|)))#

In your case, the concentration of hydronium cations is said to be equal to

#["H"_3"O"^(+)] = 2.5 * 10^(-5)"M"#

This means that the pH of the solution will be

#"pH" = - log(2.5 * 10^(-5)) = color(green)(|bar(ul(color(white)(a/a)4.6color(white)(a/a)|)))#

Now, is a pH of #4.6# characteristic of an acidic, a neutral, or a basic solution?

Aqueous solutions at room temperature exhibit the following relationship between the concentration of hydronium cations and hydroxide anions, #"OH"^(-)#

#color(blue)(|bar(ul(color(white)(a/a)["H"_3"O"^(+)] * ["OH"^(-)] = 10^(-14)"M"^2color(white)(a/a)|)))#

This relationship is based on the self-ionization of water at room temperature, for which the ionization constant, #K_W#, is equal to

#K_W = 10^(-14)"M"^2#

Now, a neutral solution will always have equal concentrations of hydronium cations and hydroxide anions. For pure water at room temperature, and taking #x# to be the concentration of the two ions, you have

#x * x = 10^(-14)"M"^2 implies x = sqrt(10^(-14)"M"^2) = 10^(-7)"M"#

So, a neutral solution has

#["H"_3"O"^(+)] = ["OH"^(-)] = 10^(-7)"M"#

In your case, you have a higher concentration of hydronium cations than you would have in a neutral solution. This means that the solution will be acidic, since it contains a higher concentration of hydronium cations than of hydroxide anions.

#["OH"^(-)] = (10^(-14)"M"^2)/(["H"_3"O"^(+)])#

In your case, you have

#["OH"^(-)] = (10^(-14)"M"^color(red)(cancel(color(black)(2))))/(2.5 * 10^(-5)color(red)(cancel(color(black)("M")))) = 4.0 * 10^(-10)"M"#

As you can see, you have

#["H"_3"O"^(+)] > ["OH"^(-)] -># the solution will be acidic